Alright, sure. Peter had a role in leading the early Church. The "bind/loose" thing is also commissioned to the rest of the disciples in Matthew 18:18. I'll be honest and say that I don't know what those keys are exactly for. But what I do know is that the Bible doesn't talk about those keys being passed down to anybody else.
This was covered a few pages back, but it doesn't hurt to repeat it.
The apostles did indeed all receive the authority to "bind and loose," but only St. Peter received the "keys of the Kingdom of Heaven," which is a direct reference to a specific office from the Old Testament.
In Isaiah 22:20-22, we see how authority worked in the Kingdom of David when King Hezekiah appoints Eliakim to the office of 'master of the palace': "I will place on his shoulder the key of the house of David; what he opens no one can shut, and what he shuts no one can open" which sounds a lot like what Jesus just told St. Peter.
The master of the palace's role was to govern the king's household on his behalf. So, he was the king's chief steward, which was the highest authority under the king himself. He managed all of the kingdom's affairs and acted with the king's own authority.
This was a permanent office that the kingdom needed to function properly. When Eliakim died, someone else would be appointed to that office to serve the next king. Except now there is no next King, Jesus is our Eternal King, and only St. Peter holds the keys to that office, he is the one who was entrusted to govern the house in the King's name.
So, if the Church needed such an office for unity and governance while the apostles were still alive, then it would certainly need one after they were gone. The keys had to be passed down, otherwise the office would have died with St. Peter and Jesus' claim that "the powers of death shall not prevail against it" would have been a lie.
And while it's not explicitly written in the Bible, the Early Christians certainly acted like the keys were passed down. I posted multiple quotes from them a few pages back.